Page 345 - HOW TO PROVE IT: A Structured Approach, Second Edition

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Appendix 1: Solutions to Selected Exercises 331
5. (a) (−3 ∈ R) ∧ (13 − 2(−3) > 1). Bound variables: x; no free variables.
This statement is true.
(b) (4 ∈ R) ∧ (4 < 0) ∧ (13 − 2(4) > 1). Bound variables: x; no free vari-
ables. This statement is false.
(c) ¬[(5 ∈ R) ∧ (13 − 2(5) > c)]. Bound variables: x; free variables: c.
7. (a) {x | Elizabeth Taylor was once married to x}= {Conrad Hilton Jr.,
Michael Wilding, Michael Todd, Eddie Fisher, Richard Burton, John
Warner, Larry Fortensky}.
(b) {x | x is a logical connective studied in Section 1.1} ={∧, ∨, ¬}.
(c) {x | x is the author of this book} = {Daniel J. Velleman}.

Section 1.4
1. (a) {3, 12}.
(b) {1, 12, 20, 35}.
(c) {1, 3, 12, 20, 35}.
The sets in parts (a) and (b) are both subsets of the set in part (c).
4. (a) Both Venn diagrams look like this:

U
A B

(b) Both Venn diagrams look like this:

U
A B

C